I do not see the "skins.res" file in that image. There, literally, must be a file named "skins.res" in the skins folder. That file contains all the known information about the skins allowed online in the game. Without that file, no skin can be used online.
The only way to get that file is to be connected online to an arena for a bit.
You will note this also happens when we release a new batch of skins. All the skins go away, then they come back once the new version of the "skins.res" file has been installed.